Table of Contents

Orbital Mechanics

Student Activity

Energy: Answer Key

1. The Space Shuttle's orbital speed is about 7.8 km/s and its mass is (typically) 180 metric tonnes. Calculate the kinetic energy of the Space Shuttle in orbit.

   ANS.: 5,5 x 10¹² J

2. One metric tonne of TNT contains 4.2 x 10⁹ joules of energy.

   • What mass of TNT would be equivalent to the kinetic energy of the space shuttle in orbit?

     ANS.: 1,3 x 10³ T! More than 1,5 times the mass of the shuttle itself.

   • Given that the kinetic energy of the space shuttle is zero when it is at rest on the landing runway, what happened to the kinetic energy?

     ANS.: It must be dissipated as heat.

3. Calculate the binding kinetic energy of a one kilogram mass on the surface of the Moon.

   ANS.: -2,7 MJ

4. Calculate the binding potential energy of a one kilogram mass on the surface of the Earth.

   ANS.: -62 MJ

5. Since the initial kinetic energy of a launched mass must be exactly equal to the binding kinetic energy of the mass, calculate the velocity needed for a one kilogram mass to

   • escape from the Earth's surface (to infinity).

     ANS.: 11,1 km/s

   • escape from the Moon's surface (to infinity).

     ANS.: 2,3 km/s

6. What would be the eccentricity of these orbits/trajectories?

   ANS.: At escape velocity the eccentricity would be exactly 1. That is, the orbits would be parabolas.

Kinetic Energy

K_e = ½ mv²

Gravitational Binding Energy

P_e = -GMm/r

G = 6,67 x 10^-11 Nm²/kg²
Radius of the Earth = 6,40 x 10⁶ m
Mass of the Earth = 5,97 x 10²⁴ kg
Mass of the Moon = 7,17 x 10²² kg
Radius of the Moon =1,74 x 10⁶ m
Mass of Mars = 6,35 x 10²³ kg
Radius of Mars = 3,40 x 10⁶ m